Subgeometric rates of convergence in Wasserstein distance for Markov\n chains

2014/02/19 by Alain Durmus, Durmus, Alain, Gersende Fort +3 · 1 citation
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1402.4577

openalex publication_date 2014/02/19 · openalex created_date 2022/09/26 · openalex updated_date 2026/07/28

Abstract

In this paper, we provide sufficient conditions for the existence of the\ninvariant distribution and for subgeometric rates of convergence in Wasserstein\ndistance for general state-space Markov chains which are (possibly) not\nirreducible. Compared to previous work, our approach is based on a purely\nprobabilistic coupling construction which allows to retrieve rates of\nconvergence matching those previously reported for convergence in total\nvariation. Our results are applied to establish the subgeometric ergodicity in\nWasserstein distance of non-linear autoregressive models and of the\npre-conditioned Crank-Nicolson Markov chain Monte Carlo algorithm in Hilbert\nspace.\n

Citations

• Renewal theory and computable convergence rates for geometrically ergodic Markov chains
• Quantitative convergence rates for sub-geometric Markov chains

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• Estimating Convergence of Markov chains with L-Lag Couplings

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